In a study with 600 high school seniors analyzing GPA and college aid using linear regression, what is the approximate degrees of freedom for the slope test?

In a study with 600 high school seniors analyzing GPA and college aid using linear regression, what is the approximate degrees of freedom for the slope test?

• A. 597 degrees of freedom
• B. 598 degrees of freedom
• C. 600 degrees of freedom
• D. 2 degrees of freedom

Answer: (B)

In simple linear regression, the test for the slope uses the residual degrees of freedom, which is the number of observations minus the number of estimated parameters. Here, two parameters are estimated: the intercept and the slope. With 600 observations, the degrees of freedom for the slope test is 600 − 2 = 598. So the best choice is 598. Why the other numbers don’t fit: 600 would be the total sample size, not the df for the slope test. 2 is just the number of coefficients estimated, not the df. 597 would imply subtracting only one parameter, which isn’t correct in this context.

In simple linear regression, the test for the slope uses the residual degrees of freedom, which is the number of observations minus the number of estimated parameters. Here, two parameters are estimated: the intercept and the slope. With 600 observations, the degrees of freedom for the slope test is 600 − 2 = 598. So the best choice is 598.

Why the other numbers don’t fit: 600 would be the total sample size, not the df for the slope test. 2 is just the number of coefficients estimated, not the df. 597 would imply subtracting only one parameter, which isn’t correct in this context.